Summary
An advanced Boundary Element formulation for eigenvalue problems of membranes and plates is developed. Polygonal membranes are considered, and are embedded into a proper basic domain in order to satisfy boundary conditions exactly as far as possible. Hence, boundary integrals have to be applied at the not coinciding boundaries only. Eigenvalues of the underlying Dirichlet's Helmholtz problem are calculated from frequency response functions evaluated by that “method with Green's functions of finite domains”, and natural frequencies of corresponding membranes and simply supported plates are determined by analogy. A numerical investigation is performed for parallelogram Mindlin plates. Natural frequencies and critical buckling eigenvalues are graphically represented in a nondimensional form, where the influence of skew angle and plate thickness is studied.
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Heuer, R., Irschik, H. A boundary element method for eigenvalue problems of polygonal membranes and plates. Acta Mechanica 66, 9–20 (1987). https://doi.org/10.1007/BF01184282
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DOI: https://doi.org/10.1007/BF01184282